If I had surgery to remove metastatic osteosarcoma from my lungs, would I need to have the whole lung removed?

Avoid. Having the whole lung removed is called a pnemonectomy. A pneumonectomy should be avoided in surgery for metastatic disease.
Not necessarily. Because it is metastatic, this surgery is often times "palliative", in other words not curative. A solitary lesion would undergo a wedge resection, removing a portion of the lung. Metastatic disease throughout lung may require total pneumonectomy. In palliative therapy one does not want to disable patient further, .